A matrix whose entries are only zeros and ones is a binary matrix. A binary matrix is said to satisfy consecutive 1's property for rows if its columns can be permuted in such a way that 1's in each row occur consecutively [1]}. For a simple undirected graph \(G=(V,E)\) , a matrix is known as the augmented adjacency matrix of \(G\)  if we replace all principal diagonal elements of the adjacency matrix of \(G\)  by 1 [2]}. A simple directed graph \(G=(V,E)\)  is an interval catch digraph (in brief, ICD) if each vertex \(u\in V\)  corresponds to a pointed interval \((I_u,p_u)\) , where \(I_u\)  is an interval on the real line and \(p_u\in I_u\) , such that \(uv\)  is an arc of \(G\)  if and only if \(u\ne v\)  and \(p_v\in I_u\) .[3]} An interval catch digraph is central if \(p_u\)  is the center point of \(I_u\)  for each \(u\in V\) . We call this graph by central interval catch digraph (in brief, CICD).In [4]}, Maehara used the term interval digraph for a CICD.
